Plasma containment apparatus comprising rotating and fixed magnetic fields



Aprll 18, 1967 THGNEMANN ET AL 3,315,] 14

PLASMA CONTAINMENT APPARATUS COMPRISING ROTATING AND FIXEDYMAGNETIC FIELDS Filed Feb. 5, 1962 2 Sheets-Sheet 1 I April 18, 1967 P c THQNEMANN ET AL 3,3l5,1 14

PLASMA CONTAINMENT APPARATUS COMPRISING ROTATING AND FIXED MAGNETTC FIELDS Filed Feb. 5. 1962 2 Sheets-Sheet 2 United States Patent 3,315,114 PLASMA CONTAINMENT APPARATUS COMPRIS- ING ROTATING AND FIXED MAGNETIC FIELDS Peter Clive Thonemann and Philip Alan Davenport, Oxford, England, and Henry Alexander Blevin, Armidale, New South Wales, Australia, assignors to United Kingdom Atomic Energy Authority, London, England Filed Feb. 5, 1962, Ser. No. 171,063 Claims priority, application Great Britain, Feb. 9, 1961, 4,891/ 61 2 Claims. (Cl. 313-161) This invention relates to plasma confinement apparatus.

For the attainment of thermonuclear power it is necessary to devise means for confining a hot plasma of a fuel gas Without the plasma coming into contact with physical boundaries.

In its broadest aspect the present invention provides plasma confinement apparatus comprising a vessel for containing a gas at low pressure, means for producing a radio-frequency rotating magnetic field within the vessel, and means for producing a stationary magnetic field within the vessel normal to the rotating magnetic field, the arrangement being such that the electrons in the plasma, but not the ions, rotate with the rotating field, thereby constituting a current which reacts with the stationary field to concentrate the plasma away from the Walls of the vessel.

According to another aspect, the present invention provides plasma confinement apparatus comprising a vessel for containing a gas at low pressure, means for producing a radio-frequency rotating field within the vessel of field strength B and angular frequency w, such that that Where n is the number of ions per unit volume of the plasma, 2 is the electronic charge and 1 is the resistivity of the plasma; and means for producing within the vessel a stationary magnetic field of strength B normal to the rotating magnetic field such that Where N is the total number of of the plasma.

The vessel is preferably of circular cross-section and may be a straight tube.

To illustrate the nature of the present invention, attention is directed, by way of example, to the accompanying drawings wherein:

FIG. 1 is a diagram illustrating the theory of the invention.

FIGS. 2, 3 and 4 are curves of magnetic field profiles and particle density distributions obtainable by means of the invention.

FIG. 5 is a partial cross-section of apparatus according to the invention with the electrical circuit shown diagrammatically.

Referring to FIG. 1, consider a straight tube 1 containing a plasma, i.e. a fully ionised gas. It is arranged, by means of a multi-phase winding on the vessel, to produce a rotating magnetic field B normal to the axis of the vessel. The field B rotates anti-clockwise with angular frequency w, as shown by the arrow.

Let n be the number of electrons (or ions) per unit volume of the plasma, e the electronic charge, and 1 the resistivity of the plasma. Also let w be chosen so that electrons per unit length Where w and w are respectively the ion and electron cyclotron frequencies corresponding to a field of strength B. This frequency limitation has the effect that the E.M.F.s induced by the rotating field B change too rapidly for the ions to respond, and only the electrons are influenced thereby.

Under these conditions it can be shown that, provided 2(% 1 j6= nerw and Where j, is the electron current per unit cross-sectional area flowing round the axis of the tube at is the electron current flowing in the axial direction. The physical meaning of this result is that the electrons rotate about the axis of the tube with the same angular velocity w as the magnetic field B. The ions do not rotate with the field, but are bound within the body of rotating electrons by space-charge forces.

The circulating current i, produces an axial magnetic field Within the vessel. If an additional uniform axial field B is applied to the vessel by means of external coils in the opposite direction to the self-field of the circulating current, an inward radial force will act on the plasma due to the interaction of j, with B As a result, it can be shown that, it N is the electron line density, i.e. the total number of electrons per unit axial length of the plasma, then the electron particles density n varies with the radius r according to the expression.

radius r, and j If N is the total number of electrons per unit length of the plasma outside radius r then Where B is the resultant axial field at radius r.

The axial field due to the circulating current alone is thus 2New at radius r, and 2N ew at the axis.

It can be shown from Equations 1 and 2 that (a) if B 2N ew, then It decreases monotonically with r, and B is unidirectional Within the vessel.

(b) if N ew B 2N ew, then It is a maximum at some distance from the axis and B reverses in the axial region, i.e. is in the opposite direction to B (If B N ew, the reversed internal field (B 2N ew) is greater than the external field (B and the plasma is forced outwards from the axis.)

Curves showing how the plasma density n and the resultant field B vary with radius r in a tube of radius R for cases (a) and (b) above are shown in FIGS. 2 and 3 respectively. It will be seen that in both cases the plasma is confined away from the walls of the tube. To reduce the number of particles escaping at the ends of the vessel, magnetic field configurations of the so-called magnetic bottle type can be arranged at the ends, such that a radial magnetic field component repulses charged particals trying to cross it in the axial direction in a manner similar to that of the so-called Mirror Machine. The configuration shown in FIG. 3 itself contributes a magnetic-bottle effect, since the reversed magnetic field in the axial region results in the magnetic field lines within the vessel curving round to form closed loops at the ends of the plasma.

For large values of r, Equation 1 reduces to an expression of the form Where A and D are constants. Thus if the radius of the vessel is made sufficiently large, virtually complete separation is obtained between the plasma and the walls, as shown in FlG. 4.

Experiments to verify the above results have been made using glass vessels 20 cm. long, and 3 and cm. in diameter, filled with argon, tenon, neon or helium at pressures of 1-50 t Hg. Rotating fields of up to 1000 gauss were produced by means of the arrangement shown in FIG. 5 in which the two pairs of parallel copper bars 2 and 3 joined at one end and arranged in mutually perpendicular planes to form a two-phase winding were energized from capacitor banks 4 and 5 through spark-gaps 6 and 7. The capacitor banks resonated with the inductance of the bars such that w was 8X10 radians/sec. (about 1.3 mc./s.).

The 90 phase difference between the currents in the windings was produced by arranging that one spark-gap fired at A1 cycle after the other. The current in the rods was a damped oscillation with a maximum value of about 7000 amps.

A steady axial magnetic field B was applied by means of the windings 8 and 9 in strengths up to 1000 gauss.

The apparatus enabled plasma particle densities of the order 4X10 /cc. to /cc. to be produced at the axis of the vessel.

Particle densities and magnetic field profiles in good agreement with Equations 1 and 2 have been measured; the particle density distributions and magnetic profiles shown in both FIGS. 2 and 3 have been observed. It will be appreciated that these confinement conditions persisted for only a few microseconds, because of the rapid decay of the rotating magnetic field. If the rotating field were maintained for a longer period the confinement conditions would be correspondingly prolonged.

Experiments using a torodial instead of a cylindrical vessel suggest that the theory is also valid in toroidal geometry, which has the advantage of avoiding end-effects.

In devices of the Stellarator or Toroidal Pinch type, confinement is poor owing to unidentified instabilities. A rotating field device of the type described could be used in conjunction with these devices to improve confinement.

We claim:

1. Plasma confinement apparatus comprising (a) a tubular vessel for containing a gas at low pressure,

(b) means for generating a radio-frequency rotating magnetic field within said vessel and normal to the length of said vessel, said rotating magnetic field being of field strength B and angular frequency w, such that whereby w and w are the ion and electron cyclotron frequencies respectively in a field of strength B, and such that new 2 2( B 1 where n is the number of ions per unit volume of the plasma, e is the electronic charge and n is the resistivity of the plasma, and (c) means for producing a stationary magnetic field within said vessel parallel to the length of said vessel and normal to said rotating magnetic field, said stationary magnetic field being of strength B such that Where N is the total number of electrons per unit length of the plasma.

2. A plasma confining apparatus as claimed in claim 1 wherein said means for generating a radio frequency rotating magnetic field comprises a first and a second winding, each winding comprising a plurality of conductors extending along the outside of said vessel parallel to the length of the vessel, said first and second windings lying in mutually perpendicular planes.

References Cited by the Examiner UNITED STATES PATENTS 2,345,115 3/1944 Hall 313-154 X 3,005,767 10/1961 Boyer et a1. 31316'1 X 3,052,614 9/1962 Herold 3l316l X 3,090,737 5/1963 Swartz 313161 3,183,398 5/1965 Hergenrother 313154 X JAMES W. LAWRENCE, Primary Examiner. ARTHUR GAUSS, DAVID J. GALVIN, Examiners. C. R. CAMPBELL, R. SEGAL, Assistant Examiners. 

1. PLASMA CONFINEMENT APPARATUS COMPRISING (A) A TUBULAR VESSEL FOR CONTAINING A GAS AT LOW PRESSURE, (B) MEANS FOR GENERATING A RADIO-FREQUENCY ROTATING MAGNETIC FIELD WITHIN SAID VESSEL AND NORMAL TO THE LENGTH OF SAID VESSEL, SAID ROTATING MAGNETIC FIELD BEING OF FIELD STRENGTH B AND ANGULAR FREQUENCY W, SUCH THAT 